Standard deviation of NDVI

Our original metric. Tells us about the spread of the distribution of NDVI on the same scale as that of the NDVI data

hetNDVI <- cbi %>%
  select(starts_with("het_ndvi"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("het_ndvi")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(hetNDVI, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(hetNDVI, aes(x = heterogeneity, y = cbi_over)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 184 rows containing non-finite values (stat_smooth).

## Warning: Removed 184 rows containing missing values (geom_point).

Standard deviation of NDWI

hetNDWI <- cbi %>%
  select(starts_with("het_ndwi"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("het_ndwi")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(hetNDWI, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(hetNDWI, aes(x = heterogeneity, y = cbi_over)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 184 rows containing non-finite values (stat_smooth).

## Warning: Removed 184 rows containing missing values (geom_point).

Entropy

“Measures the randomness of a gray-level distribution”

nd_ent <- cbi %>% 
  select(starts_with("nd_ent"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_ent")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_ent, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_ent, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Inverse difference moment

“Homogeneity. IDM tells us about the smoothness of the image.”

nd_idm <- cbi %>% 
  select(starts_with("nd_idm"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = homogeneity, starts_with("nd_idm")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_idm, aes(x = homogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_idm, aes(x = homogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Variance

“Variance tells us how spread out the distribution of gray-levels is.”

nd_var <- cbi %>% 
  select(starts_with("nd_var"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_var")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_var, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_var, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Angular second moment

“ASM measures the number of repeated pairs”

nd_asm <- cbi %>% 
  select(starts_with("nd_asm"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_asm")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_asm, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_asm, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Correlation

“Measures the correlation between the two pixels in the pixel pair”

nd_corr <- cbi %>% 
  select(starts_with("nd_corr"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_corr")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_corr, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_corr, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Contrast

“Contrast measures the local contrast of an image”

nd_contrast <- cbi %>% 
  select(starts_with("nd_contrast"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_contrast")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_contrast, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_contrast, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

savg

“sum average”

savg <- cbi %>% 
  select(starts_with("nd_savg"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_savg")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(savg, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(savg, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

svar

“sum variance”

svar <- cbi %>% 
  select(starts_with("nd_svar"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_svar")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(svar, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(svar, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

sent

“sum entropy”

sent <- cbi %>% 
  select(starts_with("nd_sent"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_sent")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(sent, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(sent, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

dvar

“difference variance”

dvar <- cbi %>% 
  select(starts_with("nd_dvar"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_dvar")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(dvar, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(dvar, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

dent

“difference entropy”

dent <- cbi %>% 
  select(starts_with("nd_dent"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_dent")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(dent, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(dent, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

imcorr1

“Info. measure of corr. 1”

imcorr1 <- cbi %>% 
  select(starts_with("nd_imcorr1"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_imcorr1")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(imcorr1, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(imcorr1, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

imcorr2

“Info. measure of corr. 2”

imcorr2 <- cbi %>% 
  select(starts_with("nd_imcorr2"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_imcorr2")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(imcorr2, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(imcorr2, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

dissimilarity

“dissimilarity”

nd_diss <- cbi %>% 
  select(starts_with("nd_diss"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_diss")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_diss, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_diss, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

inertia

“intertia”

nd_inertia <- cbi %>% 
  select(starts_with("nd_inertia"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_inertia")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_inertia, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_inertia, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

shade

“cluster shade”

nd_shade <- cbi %>% 
  select(starts_with("nd_shade"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_shade")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_shade, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_shade, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).

Prominence

“cluster prominence”

nd_prom <- cbi %>% 
  select(starts_with("nd_prom"), cbi_over, id, RBR) %>% 
  gather(key = radius, value = heterogeneity, starts_with("nd_prom")) %>% 
  separate(col = radius, into = c("type", "vi", "radius")) %>% 
  tidyr::unite(het_type, type, vi, sep = "_")

ggplot(nd_prom, aes(x = heterogeneity)) +
  geom_density() + 
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_density).

ggplot(nd_prom, aes(x = heterogeneity, y = RBR)) +
  geom_point() + 
  geom_smooth(method = "lm") +
  facet_wrap( ~ as.factor(radius))

## Warning: Removed 32 rows containing non-finite values (stat_smooth).

## Warning: Removed 32 rows containing missing values (geom_point).